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NASA NTRS1977

Gravitational radiation from binary systems in alternative metric theories of gravity - Dipole radiation and the binary pulsar

The generation of gravitational radiation in several currently viable metric theories of gravitation (Brans-Dicke, Rosen, Ni, and Lightman-Lee) is analyzed, and it is shown that these theories predict the emission of dipole gravitational radiation from systems containing gravitationally bound objects. In the binary system PSR 1913 + 16, this radiation results in a secular change in the orbital period of the system with a nominal magnitude of 3 parts in 100,000 per year. The size of the effect is proportional to the reduced mass of the system, to the square of the difference in (self-gravitational energy)/(mass) between the two components of the system, and to a parameter, xi, whose value varies from theory to theory. In general relativity xi equals 0, in Rosen's (1973) theory xi equals -20/3, and in Ni's (1973) theory xi equals -400/3. The current upper limit on such a secular period change is one part in 1 million per year. It is shown that further observations of the binary system that tighten this limit and that establish the masses of the components and the identity of the companion may provide a crucial test of otherwise viable alternatives to general relativity.

Will, C. M.↗

NASA NTRS1977

Evaluation of the Tensor Polynomial and Hoffman strength theories for composite materials

The Hoffman theory and the Tensor Polynomial (Tsai-Wu) theory with the stress interaction term set equal to zero have been found to be preferred alternatives to the general Tensor Polynomial theory for predicting strength of filamentary composite laminae. These theories were used to predict failure of off-axis boron/epoxy and E-glass/epoxy test specimens and gave excellent agreement with available experimental results. A numerical experiment was also performed to estimate the errors for ten different composite systems under six different loadings. The maximum error in predicted failure loads among all cases was below 10 percent. These results suggest that the Hoffman failure theory and the Tensor Polynomial theory with the stress interaction term equal to zero can predict failure of practical filamentary composite materials under general biaxial loading with sufficient accuracy for engineering applications.

Narayanaswami, R.↗

NASA NTRS1978

A comparison of three classical analytical theories for the motion of artificial satellites

Motivated by the heavy reliance upon the analytic orbit theory in orbit determination operations at the Goddard Space Flight Center (GSFC), a comparison study is performed for three classical analytical theories of artificial satellite motion about an oblate earth. The three analytical theories are: (1) Brouwer, (2) a modified Brouwer, i.e., Brouwer-Lyddane and Cohen, and (3) Vinti. Comparison results for each theory are produced for a number of representative satellites of current or past interest which proved amenable to analytic theory application. The uniformity of these results has significant implications for current and future mission operations and planning activities. Subsidiary topics arising from the results of this study which relate to the optimum usage of the individual theories are also discussed

Gordon, R. A.↗

NASA NTRS1979

Application of supersonic linear theory and hypersonic impact methods to three nonslender hypersonic airplane concepts at Mach numbers from 1.10 to 2.86

Aerodynamic predictions from supersonic linear theory and hypersonic impact theory were compared with experimental data for three hypersonic research airplane concepts over a Mach number range from 1.10 to 2.86. The linear theory gave good lift prediction and fair to good pitching-moment prediction over the Mach number (M) range. The tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone/tangent-wedge method gave the least accurate prediction of lift and pitching moment. The zero-lift drag was overestimated, especially for M less than 2.0. The linear theory drag prediction was generally poor, with areas of good agreement only for M less than or equal to 1.2. For M more than or equal to 2.), the tangent-cone method predicted the zero-lift drag most accurately.

Pittman, J. L.↗

NASA NTRS1980

A comparison between an existing propeller noise theory and wind tunnel data

The noise of three supersonic helical tip speed propellers was compared with the noise predicted by an existing noise theory. Comparisons of the peak blade passage tones showed fairly good agreement beween theory and experiment at the lowest helical tip Mach numbers tested, 0.86 and 1.00, while at higher numbers, the theory predicted higher noise levels than measured. When the differences among the propellers were considered the theory and measurement showed fairly good agreement. Directivity measurements in general showed that the measured blade passage tone data peaked further downstream than the theory predicted. At the cruise design condition the harmonics appeared to fall off faster in the data than the theory indicated.

Dittmar, J. H.↗

NASA NTRS1981

Comparison of theory and in situ observations for electron and ion distributions in the near wake of the Explorer 31 and AE-C satellites

Measurements of electron density, plasma potential, and mean ion mass from the Explorer 31 satellite, and measurements of ion current, plasma potential, and ion composition from the Atmosphere Explorer C satellite were used in a comparative study with Parker's theory regarding the charged particle distribution in the near wake of an ionospheric satellite (1976). It is shown that theory and experiment agree fairly well in the angle-of-attack range between 90 and 135 deg. In the maximum rarefaction zone (between 145 and 180 deg), however, the theoretical model overestimates the measured ion depletion by several orders of magnitude. A comparison between theory and the Explorer 31 electron measurements shows that the theory again overestimates the electron depletion. These discrepancies are mainly due to the use of a steady-state theory and a single ion equation (using a mean ion mass). Improved agreement between theory and experiment can be obtained by the use of the time-dependent Vlasov-Poisson equations with separate equations for the various ion species.

Samir, U.↗

NASA NTRS1982

Comparison of beam and shell theories for the vibrations of thin turbomachinery blades

Vibration analysis of turbomachinery blades has traditionally been carried out by means of beam theory. In recent years two-dimensional methods of blade vibration analysis have been developed, most of which utilize finite elements and tend to require considerable computation time. More recently a two-dimensional method of blade analysis has evolved which does not require finite elements and is based upon shell equations. The present investigation has the primary objective to demonstrate the accuracy and limitations of blade vibration analyses which utilize one-dimensional, beam theories. It is found that beam theory is generally inadequate to determine the free vibration frequencies and mode shapes of moderate to low aspect ratio turbomachinery blades. The shallow shell theory, by contrast, is capable of representing all the vibration modes accurately. However, the one-dimensional beam theory has an important advantage over the two-dimensional shell theory for blades and vibration modes. It uses fewer degrees of freedom, thus requiring less computer time.

Leissa, A. W.↗

NASA NTRS1984

A simple higher-order theory for laminated composite plates

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

Reddy, J. N.↗

NASA NTRS1984

Rotary-wing aerodynamics. Volume 1 - Basic theories of rotor aerodynamics (With application to helicopters). Volume 2 Performance prediction of helicopters (2nd revised and enlarged edition)

Basic theories of rotor aerodynamics are presented and applied to the performance prediction of helicopters. The very simple physicomathematical model of the rotor offered by momentum theory is addressed first, followed by the combined blade-element and momentum theory. Vortex theory is discussed, and a rotor blade is modeled by means of a vortex filament or vorticity surface. Considerations of airfoil sections suitable for rotors are examined. Detailed performance techniques for a single-rotor helicopter in hover, vertical ascent, and forward flight are described, and winged and tandem-rotor helicopter performance calculations are presented as extensions and modifications of single-rotor methodology. Computer data based on the vortex theory are compared with approximate results obtained from the simplified momentum theory and the blade element solution.

Stepniewski, W. Z.↗

NASA NTRS1985

Theory of interparticle correlations in dense, high-temperature plasmas. V - Electric and thermal conductivities

Ichimaru et al. (1985) have developed a general theory in which the interparticle correlations in dense, high-temperature multicomponent plasmas were formulated systematically over a wide range of plasma parameters. The present paper is concerned with an extension of this theory, taking into account the problems of the electronic transport in such high-density plasmas. It is shown that the resulting theory is capable of describing the transport coefficients accurately over a wide range of the density and temperature parameters. Attention is given to electric and thermal conductivities, generalized Coulomb logarithms, a comparison of the considered theory with other theories, and a comparison of the theory with experimental results.

Ichimaru, S.↗

NASA NTRS1986

A refined shear deformation theory for the analysis of laminated plates

A refined, third-order plate theory that accounts for the transverse shear strains is presented, the Navier solutions are derived for certain simply supported cross-ply and antisymmetric angle-ply laminates, and finite-element models are developed for general laminates. The new theory does not require the shear correction factors of the first-order theory (i.e., the Reissner-Mindlin plate theory) because the transverse shear stresses are represented parabolically in the present theory. A mixed finite-element model that uses independent approximations of the generalized displacements and generalized moments, and a displacement model that uses only the generalized displacements as degrees of freedom are developed. The displacement model requires C sup 1-continuity of the transverse deflection across the inter-element boundaries, whereas the mixed model requires a C sup 0-element. Also, the mixed model does not require continuous approximations (between elements) of the bending moments. Numerical results are presented to show the accuracy of the present theory in predicting the transverse stresses. Numerical results are also presented for the nonlinear bending of plates, and the results compare well with the experimental results available in the literature.

Reddy, J. N.↗

NASA NTRS1987

Application of ray theory to propagation of low frequency noise from wind turbines

Ray theory is used to explain data from two experiments (1985 and 1985) on the propagation of low frequency sound generated by the WTS-4 wind turbine. Emphasis is on downwind data, but some upwind measurements taken during the 1985 experiment are also considered. General ray theory for a moving medium is reviewed and ray equations obtained. Restrictions are introduced simplifying the equations and permitting the use of a ray theory program MEDUSA, the computed propagation loss curve of which is compared to the measurements. Good qualitative agreement is obtained with 1984 downwind data. The results indicate that the downwind sound field is that of a near-ground sound channel. Although more scatter is seen in the 1985 data, agreement between theory and data is also good. In particular, the position and magnitude of the jump in the sound levels associated with the beginning of the sound channel is correctly predicted. The theoretical explanation of the upwind data is less successful. Ray theory calculations indicate the formation of a shadow zone that, in fact, does not occur. While no sharp shadow zone is apparent in the data, the general expectation (based on ray theory) that sound levels should be much reduced upwind is confirmed by the data.

Hawkins, James A.↗

NASA NTRS1988

Aerosol measurements in the winter/spring Antarctic stratosphere. I - Correlative measurements with ozone. II - Impact on polar stratospheric cloud theories

Aerosol measurements collected from August 25-November 3, 1986 at McMurdo Station using balloon-borne optical particle counters are examined in order to study the relationship between aerosol and ozone distribution and the formation of polar stratospheric clouds (PSCs). Ozone, aerosol, and condensation nuclei profiles, and pressure, temperature, and humidity measurements are analyzed. It is observed that the height of the stratospheric sulfate layer decreases over the period of measurement suggesting that upwelling in the votex is not important in the zone depletion process. Three theories on PSC formation are described, and the effects of the aerosol measurements on the theories are considered. The three theories are: (1) the original theory of water vapor pressure over a solution of H2SO4 of Steele et al. (1983) and Hamill and Mc Master (1984); (2) the nitric acid theory of PSCs of Toon et al. (1986) and Hamill et al. (1986); and (3) the quasi-cirrus cloud theory of Heymsfield (1986).

Hofmann, D. J.↗

NASA NTRS1988

Theory of anisotropic refractive scintillation - Application to stellar occultations by Neptune

A theory of refractive scintillation due to a thin phase-changing screen with an anisotropic power-law spectrum of phase fluctuations is presented. Scintillation theory for an isotropic medium is discussed, and anisotropy of the mean density and anisotropy in the scattering are discussed. The theory of refractive scintillation in an anisotropic medium is developed, deriving a general expression for the cross-correlation of flux variations at two points on the 'observer screen'. From this, estimates of the coherence lengths and amplitudes of flux variations are obtained for important parameter regimes. The application of the theory to the analysis of two occultations by Neptune is addressed. The projected dimensions of the occulting stars, a normalization constant to describe the phase fluctuations, and an anisotropy parameter are determined, and the theory is shown to agree well with observation. The significance of the theory for understanding of the physics of Neptune's atmosphere is discussed.

Narayan, Ramesh↗

NASA NTRS1994

Mode properties of low-frequency waves: Kinetic theory versus Hall-MHD

In fluid theory, the ordering of low-frequency modes in a homogeneous plasma is based on the phase velocity, since modes do not intersect each other in dispersion diagrams as a function of wavenumber or other parameters. In linear kinetic theory, modes cross each other. Thus a consistent and useful classification should be based on the physical properties of the modes instead. This paper attempts such a classification by documeting the dispersion and general mode properties of the low-frequency waves (omega much less than (OMEGA(sub ci) OMEGA(sub ce) (exp 1/2)), where OMEGA(sub ci), OMEGA(sub ce) are the cyclotron frequencies of the ions and electrons, respectively) in kinetic theory, and by comparing them to the results of two-fluid theory. Kinetic theory gives a seperate Alfven/ion-cyclotron (A/IC) wave with phase speed Omega/k approximately = v(sub A) cos theta for omega much less than OMEGA(sub ci), where v(sub A) is the Alfven velocity and theta the angle of propagation between wave vector k and background magnetic field B(sub o). For a given wavenumber, the magnetosonic mode is a double-valued solution with a singular point in theta, beta parameter space, where beta is the ratio of thermal pressure to magnetic pressure. It is shown that a branch cut starting at the singular point theta approximately 30 deg, beta approximately 3 and leading to larger beta gives a practical and consitent seperation of this double-valued magnetosonic solution. Selection of this branch cut results in a moderately damped fast/magnetos onic and a heavily damped slow/sound wave. A comprehensive review of the polarization, compressibility and other mode properties is given and shown to be consistent with the selected branch cut. At small wavenumbers, the kinetic mode properties typically start to deviate significantly from their fluid counterparts at beta approximately 0.5. At larger beta, there is no longer a consistent correspondence between the fluid and kinetic modes. Kinetic theory also dictates the use of different mode properties to distinguish between them in observational data. For example, the phase between the density and magnetic field perturbation may become useless at high beta, whereas the direction of the magnetic field perturbations with respect to k and B(sub o) remains a useful characteristic. Two quantities based on this characteristic are suggested and are shown to be useful also to distinguish between the mirror mode and A/IC waves in a plasma with temperature anisotropy.

Krauss-Varban, D.↗

NASA NTRS1998

Some Comments on the Status of Shell Theory at the End of the 20th Century: Complaints and Correctives

This review is divided into complaints and correctives. Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the mis-naming or mis-crediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory are fundamentally different from 3-dimensional elasticity; and the irrelevance of Cosserat-type theories. Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics (and those of thermodynamics, if desired) are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations (including the Kirchhoff Hypothesis) occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally. (These latter two special cases are known to produce numerical nightmares unless treated with great care); and (5) all equations may be expressed in coordinate-free form (although, sometimes, a hybrid form is shown to be superior).

Simmonds, James G.↗

NASA NTRS1995

A New Theory of Nucleate Pool Boiling in Arbitrary Gravity

Heat transfer rates specific to nucleate pool boiling under various conditions are determined by the dynamics of vapour bubbles that are originated and grow at nucleation sites of a superheated surface. A new dynamic theory of these bubbles has been recently developed on the basis of the thermodynamics of irreversible processes. In contrast to other existing models based on empirically postulated equations for bubble growth and motion, this theory does not contain unwarrantable assumptions, and both the equations are rigorously derived within the framework of a unified approach. The conclusions of the theory are drastically different from those of the conventional models. The bubbles are shown to detach themselves under combined action of buoyancy and a surface tension force that is proven to add to buoyancy in bubble detachment, but not the other way round as is commonly presumed. The theory ensures a sound understanding of a number of so far unexplained phenomena, such as effect caused by gravity level and surface tension on the bubble growth rate and dependence of the bubble characteristics at detachment on the liquid thermophysical parameters and relevant temperature differences. The theoretical predictions are shown to be in a satisfactory qualitative and quantitative agreement with observations. When being applied to heat transfer at nucleate pool boiling, this bubble dynamic theory offers an opportunity to considerably improve the main formulae that are generally used to correlate experimental findings and to design boiling heat removal in various industrial applications. Moreover, the theory makes possible to pose and study a great deal of new problems of essential impact in practice. Two such problems are considered in detail. One problem concerns the development of a principally novel physical model for the first crisis of boiling. This model allows for evaluating critical boiling heat fluxes under various conditions, and in particular at different gravity levels, with a good agreement with experimental evidence. The other problem bears upon equilibrium shapes of a detached bubble near a heated surface in exceedingly low gravity. In low gravity or in weightlessness, the bubble can remain in the close vicinity of the surface for a long time, and its shape is greatly affected by the Marangoni effect due to both temperature and possible surfactant concentration being nonuniform along the interface. The bubble performs at these conditions like a heat pipe, with evaporation at the bubble lower boundary and condensation at its upper boundary, and ultimately ensures a substantial increase in heat removal as compared with that in normal gravity. Some other problems relevant to nucleate pool and forced convection boiling heat transfer are also discussed.

Buyevich, Y. A.↗

NASA NTRS2004

Product Distribution Theory for Control of Multi-Agent Systems

Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.

Lee, Chia Fan↗